The classic English linguistic definition of friendship is Webster's: friendship is "a relationship of mutual regard." Webster is concise, but emotionless, and falls short of the rich reality of friendship.
Friendship is not simply a "relationship", knowing someone, conversing with that person, or dealing with that person in business, school, or in casual acquaintance. True friendship is not just a "relationship", but self-sacrificing love.
St. Thomas Aquinas taught that friendship is the highest form of love for another human person, since it is totally without self-interest. It is a relationship that rejoices in the other person, without any requirement that the friend do something in return. The providing of entertainment or pleasure, or the gratifying of the desires or wants of the other is not a basic requirement for true friendship. True friends find joy simply in being with each other, and full joy in giving of themselves for each other.
St. Augustine saw friendship as a spiritual relationship between two people, one that was based on love, leading each friend to work for the other's happiness. Friendship is an image of God's love for us, according to Augustine, since authentic, self-sacrificing friendship mirrors the love that Christ showed for us on the Cross, and which He described teaching that "no greater love can one have than to lay down one's life for one's friend" (John 15:13). Augustine even believed that only true friendship, of everything that exists in the natural, created world, could lead one to God.
What is friendship? It is more than Webster
described, because it is a reciprocal love of one person for
another, which is disinterested. It is a love that does not look
for anything in return for the love given, and finds happiness in
promoting the interests and happiness of the other. Such a love
warms the heart, thrills the mind, and urges the friend to give
everything for the other--just as Christ does for us--and leads
to happiness in this world while pointing to God, who, Himself,
You learn to speak by speaking,
to study by studying,
to run by running,
to work by working;
and just so you learn to love God
and man by loving.
Begin as a mere apprentice,
and the very power of love
will lead you on to become
a master of the art.
St. Francis of Sales (1567-1622)